Am wondering why EA App version doesn't work for me, but GOG might?
Don't quote me on this, but based on my experiences with GOG they basically offer newer versions of old games with community patches and OS fixes preinstalled. I can't say if that is the case with Jade Empire specifically, but from what other people are saying it looks like it is.
When I wanted to play Vampire: The Masquerade Bloodlines a few years ago, the GOG version was the only one that would work on my machine!
Regarding your current copy, you can contact EA support and explain your situation. They will most likely offer a refund on you purchase and you can use that money to buy the GOG version.